NAG Library Routine Document
f07tjf (dtrtri) computes the inverse of a real triangular matrix.
|Integer, Intent (In)||:: ||n, lda|
|Integer, Intent (Out)||:: ||info|
|Real (Kind=nag_wp), Intent (Inout)||:: ||a(lda,*)|
|Character (1), Intent (In)||:: ||uplo, diag|
The routine may be called by its
f07tjf (dtrtri) forms the inverse of a real triangular matrix . Note that the inverse of an upper (lower) triangular matrix is also upper (lower) triangular.
Du Croz J J and Higham N J (1992) Stability of methods for matrix inversion IMA J. Numer. Anal. 12 1–19
- 1: – Character(1)Input
: specifies whether
is upper or lower triangular.
- is upper triangular.
- is lower triangular.
- 2: – Character(1)Input
: indicates whether
is a nonunit or unit triangular matrix.
- is a nonunit triangular matrix.
- is a unit triangular matrix; the diagonal elements are not referenced and are assumed to be .
- 3: – IntegerInput
On entry: , the order of the matrix .
- 4: – Real (Kind=nag_wp) arrayInput/Output
the second dimension of the array a
must be at least
- If , is upper triangular and the elements of the array below the diagonal are not referenced.
- If , is lower triangular and the elements of the array above the diagonal are not referenced.
- If , the diagonal elements of are assumed to be , and are not referenced.
On exit: is overwritten by , using the same storage format as described above.
- 5: – IntegerInput
: the first dimension of the array a
as declared in the (sub)program from which f07tjf (dtrtri)
- 6: – IntegerOutput
unless the routine detects an error (see Section 6
Error Indicators and Warnings
If , argument had an illegal value. An explanatory message is output, and execution of the program is terminated.
Element of the diagonal is exactly zero.
is singular its inverse cannot be computed.
The computed inverse
is a modest linear function of
is the machine precision
Note that a similar bound for cannot be guaranteed, although it is almost always satisfied.
The computed inverse satisfies the forward error bound
See Du Croz and Higham (1992)
Parallelism and Performance
f07tjf (dtrtri) makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the X06 Chapter Introduction
for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note
for your implementation for any additional implementation-specific information.
The total number of floating-point operations is approximately .
The complex analogue of this routine is f07twf (ztrtri)
This example computes the inverse of the matrix
Program Text (f07tjfe.f90)
Program Data (f07tjfe.d)
Program Results (f07tjfe.r)